Subgroups — C₁₃₁×#34238 #45720122

Order 33536.

2742 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#123×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	#2374×C₁₃₁	C₂	1	4	yes	maximal, complemented
3	#2359×C₁₃₁	C₂	1	4	yes	maximal, complemented
4	#2345×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2342×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2342×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	D₄×C₂²⋊C₄×C₁₃₁	C₂	1	2	yes	maximal
8	#2335×C₁₃₁	C₂	1	4	yes	maximal, complemented
9	#2313×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#2312×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#123×C₁₃₁	C₂	1	4	yes	maximal, complemented
12	#2280×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#2274×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#2273×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₂²⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
18	C₂×#123×C₁₃₁	C₄	1	16	yes	complemented
19	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
20	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
21	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
22	C₂×#123×C₁₃₁	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₃₁	C₂²	1	4	yes	—
24	C₂×#117×C₁₃₁	C₂²	1	2	yes	—
25	C₂×#117×C₁₃₁	C₂²	1	2	yes	complemented
26	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₃₁	C₂²	1	2	yes	complemented
34	#390×C₁₃₁	C₂²	1	4	yes	—
35	#389×C₁₃₁	C₂²	1	4	yes	complemented
36	#388×C₁₃₁	C₂²	1	4	yes	complemented
37	#388×C₁₃₁	C₂²	1	4	yes	complemented
38	#388×C₁₃₁	C₂²	1	4	yes	complemented
39	#388×C₁₃₁	C₂²	1	4	yes	complemented
40	#388×C₁₃₁	C₂²	1	4	yes	complemented
41	#388×C₁₃₁	C₂²	1	4	yes	complemented
42	#387×C₁₃₁	C₂²	1	4	yes	complemented
43	#387×C₁₃₁	C₂²	1	4	yes	complemented
44	#387×C₁₃₁	C₂²	1	4	yes	complemented
45	#387×C₁₃₁	C₂²	1	4	yes	complemented
46	#386×C₁₃₁	C₂²	1	4	yes	—
47	#386×C₁₃₁	C₂²	1	4	yes	—
48	#385×C₁₃₁	C₂²	1	4	yes	complemented
49	#385×C₁₃₁	C₂²	1	4	yes	complemented
50	#381×C₁₃₁	C₂²	1	2	yes	—
51	#381×C₁₃₁	C₂²	1	2	yes	complemented
52	#380×C₁₃₁	C₂²	1	2	yes	—
53	#380×C₁₃₁	C₂²	1	2	yes	—
54	#380×C₁₃₁	C₂²	1	2	yes	—
55	#380×C₁₃₁	C₂²	1	2	yes	complemented
56	#379×C₁₃₁	C₂²	1	2	yes	—
57	#379×C₁₃₁	C₂²	1	2	yes	—
58	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
59	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
60	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
61	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
66	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
68	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
71	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
72	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
73	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
74	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	4	yes	complemented
75	C₂×#95×C₁₃₁	C₂²	1	2	yes	complemented
76	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
77	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₁₃₁	—	4	4	no	—
79	C₂²×D₄×C₁₃₁	C₂×C₄	1	8	yes	—
80	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
81	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₃₁	—	4	4	no	—
83	C₂³×C₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
84	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
85	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
89	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
95	#123×C₁₃₁	C₂×C₄	1	16	yes	complemented
96	#123×C₁₃₁	C₂×C₄	1	16	yes	complemented
97	#123×C₁₃₁	C₂×C₄	1	16	yes	complemented
98	#123×C₁₃₁	C₂×C₄	1	16	yes	complemented
99	C₄×D₄×C₁₃₁	—	4	8	no	—
100	#117×C₁₃₁	—	2	8	no	—
101	#117×C₁₃₁	—	4	4	no	—
102	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
103	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
104	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₁₃₁	—	2	8	no	—
113	C₂×C₂²⋊C₄×C₁₃₁	—	2	8	no	—
114	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
115	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
116	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
117	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃₁	—	4	4	no	—
134	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
135	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
138	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
139	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
140	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
141	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
142	#95×C₁₃₁	C₂³	1	4	yes	—
143	#95×C₁₃₁	C₂³	1	2	yes	—
144	#95×C₁₃₁	C₂³	1	2	yes	—
145	#95×C₁₃₁	C₂³	1	4	yes	—
146	#95×C₁₃₁	C₂³	1	4	yes	—
147	#95×C₁₃₁	C₂³	1	4	yes	—
148	#95×C₁₃₁	C₂³	1	4	yes	—
149	#95×C₁₃₁	C₂³	1	4	yes	—
150	#95×C₁₃₁	C₂³	1	4	yes	—
151	#95×C₁₃₁	C₂³	1	2	yes	—
152	#95×C₁₃₁	C₂³	1	2	yes	—
153	#95×C₁₃₁	C₂³	1	4	yes	—
154	C₂⁴×C₁₃₁	—	2	4	no	—
155	C₂⁴×C₁₃₁	—	2	4	no	—
156	C₂⁴×C₁₃₁	—	2	4	no	—
157	C₂⁴×C₁₃₁	—	4	2	no	—
158	C₂⁴×C₁₃₁	—	4	2	no	—
159	C₂⁴×C₁₃₁	—	4	2	no	—
160	C₂⁴×C₁₃₁	C₂²×C₄	1	4	yes	—
161	C₂⁴×C₁₃₁	C₂²×C₄	1	4	yes	—
162	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
163	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
164	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
165	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
166	C₂×D₄×C₁₃₁	—	2	8	no	—
167	C₂×D₄×C₁₃₁	—	4	4	no	—
168	C₂×D₄×C₁₃₁	—	4	16	no	—
169	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
170	C₂×D₄×C₁₃₁	C₂²×C₄	1	8	yes	—
171	C₂²×C₄×C₁₃₁	—	2	4	no	—
172	C₂²×C₄×C₁₃₁	—	2	4	no	—
173	C₂²×C₄×C₁₃₁	—	2	4	no	—
174	C₂²×C₄×C₁₃₁	—	2	8	no	—
175	C₂²×C₄×C₁₃₁	—	2	8	no	—
176	C₂²×C₄×C₁₃₁	—	2	8	no	—
177	C₂²×C₄×C₁₃₁	—	4	16	no	—
178	C₂²×C₄×C₁₃₁	—	4	2	no	—
179	C₂²×C₄×C₁₃₁	—	4	2	no	—
180	C₂²×C₄×C₁₃₁	—	4	2	no	—
181	C₂²×C₄×C₁₃₁	—	4	2	no	—
182	C₂²×C₄×C₁₃₁	—	4	2	no	—
183	C₂²×C₄×C₁₃₁	—	4	4	no	—
184	C₂²×C₄×C₁₃₁	—	4	2	no	—
185	C₂²×C₄×C₁₃₁	—	4	4	no	—
186	C₂²×C₄×C₁₃₁	—	4	4	no	—
187	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
188	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
189	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
190	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
191	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
193	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
194	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
195	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
196	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
207	C₄⋊C₄×C₁₃₁	—	2	8	no	—
208	C₄⋊C₄×C₁₃₁	—	4	4	no	—
209	C₄⋊C₄×C₁₃₁	—	4	4	no	—
210	C₄⋊C₄×C₁₃₁	—	4	4	no	—
211	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
212	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
213	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
214	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
215	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
216	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
217	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
218	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
219	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
220	C₂²⋊C₄×C₁₃₁	—	2	8	no	—
221	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
222	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
223	C₂²⋊C₄×C₁₃₁	—	4	4	no	—
224	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
225	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
226	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
227	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
228	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
229	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	8	yes	—
230	C₂²⋊C₄×C₁₃₁	#41	1	8	yes	—
231	C₄²×C₁₃₁	—	2	8	no	—
232	C₄²×C₁₃₁	—	4	2	no	—
233	C₄²×C₁₃₁	—	4	4	no	—
234	C₄²×C₁₃₁	—	4	2	no	—
235	C₄²×C₁₃₁	—	4	4	no	—
236	C₄²×C₁₃₁	—	4	2	no	—
237	C₄²×C₁₃₁	—	4	2	no	—
238	C₄²×C₁₃₁	—	4	4	no	—
239	C₂³×C₁₃₁	—	2	2	no	—
240	C₂³×C₁₃₁	—	2	2	no	—
241	C₂³×C₁₃₁	—	2	2	no	—
242	C₂³×C₁₃₁	—	2	2	no	—
243	C₂³×C₁₃₁	—	2	8	no	—
244	C₂³×C₁₃₁	—	2	8	no	—
245	C₂³×C₁₃₁	—	2	2	no	—
246	C₂³×C₁₃₁	—	2	2	no	—
247	C₂³×C₁₃₁	—	2	2	no	—
248	C₂³×C₁₃₁	—	2	4	no	—
249	C₂³×C₁₃₁	—	2	2	no	—
250	C₂³×C₁₃₁	—	2	2	no	—
251	C₂³×C₁₃₁	—	2	4	no	—
252	C₂³×C₁₃₁	—	2	8	no	—
253	C₂³×C₁₃₁	—	4	4	no	—
254	C₂³×C₁₃₁	—	4	4	no	—
255	C₂³×C₁₃₁	—	4	4	no	—
256	C₂³×C₁₃₁	—	4	16	no	—
257	C₂³×C₁₃₁	—	8	8	no	—
258	C₂³×C₁₃₁	C₂³×C₄	1	4	yes	—
259	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
260	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
261	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
262	C₂³×C₁₃₁	C₂×#41	1	4	yes	—
263	C₂³×C₁₃₁	H(5,𝔽₂)	1	4	yes	—
264	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
265	D₄×C₁₃₁	—	2	16	no	—
266	D₄×C₁₃₁	—	4	8	no	—
267	C₂×C₄×C₁₃₁	—	2	8	no	—
268	C₂×C₄×C₁₃₁	—	2	8	no	—
269	C₂×C₄×C₁₃₁	—	2	8	no	—
270	C₂×C₄×C₁₃₁	—	2	2	no	—
271	C₂×C₄×C₁₃₁	—	2	2	no	—
272	C₂×C₄×C₁₃₁	—	2	4	no	—
273	C₂×C₄×C₁₃₁	—	2	2	no	—
274	C₂×C₄×C₁₃₁	—	2	2	no	—
275	C₂×C₄×C₁₃₁	—	2	2	no	—
276	C₂×C₄×C₁₃₁	—	2	4	no	—
277	C₂×C₄×C₁₃₁	—	2	2	no	—
278	C₂×C₄×C₁₃₁	—	2	4	no	—
279	C₂×C₄×C₁₃₁	—	2	4	no	—
280	C₂×C₄×C₁₃₁	—	2	4	no	—
281	C₂×C₄×C₁₃₁	—	2	4	no	—
282	C₂×C₄×C₁₃₁	—	2	4	no	—
283	C₂×C₄×C₁₃₁	—	2	4	no	—
284	C₂×C₄×C₁₃₁	—	2	4	no	—
285	C₂×C₄×C₁₃₁	—	2	4	no	—
286	C₂×C₄×C₁₃₁	—	2	4	no	—
287	C₂×C₄×C₁₃₁	—	2	4	no	—
288	C₂×C₄×C₁₃₁	—	2	4	no	—
289	C₂×C₄×C₁₃₁	—	4	4	no	—
290	C₂×C₄×C₁₃₁	—	4	4	no	—
291	C₂×C₄×C₁₃₁	—	4	4	no	—
292	C₂×C₄×C₁₃₁	—	4	4	no	—
293	C₂×C₄×C₁₃₁	—	4	4	no	—
294	C₂×C₄×C₁₃₁	—	4	4	no	—
295	C₂×C₄×C₁₃₁	—	4	16	no	—
296	C₂×C₄×C₁₃₁	—	8	8	no	—
297	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
298	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
299	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
300	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
301	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
302	C₂×C₄×C₁₃₁	C₂³×C₄	1	2	yes	—
303	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
304	C₂×C₄×C₁₃₁	C₂×#41	1	8	yes	—
305	C₂²×C₁₃₁	—	2	2	no	—
306	C₂²×C₁₃₁	—	2	2	no	—
307	C₂²×C₁₃₁	—	2	2	no	—
308	C₂²×C₁₃₁	—	2	2	no	—
309	C₂²×C₁₃₁	—	2	8	no	—
310	C₂²×C₁₃₁	—	2	8	no	—
311	C₂²×C₁₃₁	—	2	2	no	—
312	C₂²×C₁₃₁	—	2	4	no	—
313	C₂²×C₁₃₁	—	2	2	no	—
314	C₂²×C₁₃₁	—	2	4	no	—
315	C₂²×C₁₃₁	—	2	2	no	—
316	C₂²×C₁₃₁	—	2	4	no	—
317	C₂²×C₁₃₁	—	4	16	no	—
318	C₂²×C₁₃₁	—	4	4	no	—
319	C₂²×C₁₃₁	—	4	4	no	—
320	C₂²×C₁₃₁	—	4	4	no	—
321	C₂²×C₁₃₁	—	8	8	no	—
322	C₂²×C₁₃₁	C₄×#41	1	4	yes	—
323	C₂²×C₁₃₁	#518	1	4	yes	—
324	C₂²×C₁₃₁	C₂⁴×C₄	1	1	yes	characteristic
325	C₂²×C₁₃₁	C₂²×#41	1	2	yes	—
326	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
327	C₂²×C₁₃₁	#585	1	2	yes	—
328	C₄×C₁₃₁	—	2	4	no	—
329	C₄×C₁₃₁	—	2	2	no	—
330	C₄×C₁₃₁	—	2	2	no	—
331	C₄×C₁₃₁	—	2	2	no	—
332	C₄×C₁₃₁	—	2	2	no	—
333	C₄×C₁₃₁	—	2	4	no	—
334	C₄×C₁₃₁	—	2	4	no	—
335	C₄×C₁₃₁	—	2	8	no	—
336	C₄×C₁₃₁	—	4	4	no	—
337	C₄×C₁₃₁	—	4	4	no	—
338	C₄×C₁₃₁	—	4	4	no	—
339	C₂×C₁₃₁	—	2	4	no	—
340	C₂×C₁₃₁	—	2	4	no	—
341	C₂×C₁₃₁	—	4	2	no	—
342	C₂×C₁₃₁	—	4	4	no	—
343	C₂×C₁₃₁	C₂×C₄×#41	1	1	yes	characteristic
344	C₂×C₁₃₁	C₂×#518	1	1	yes	characteristic
345	C₂×C₁₃₁	#3428	1	1	yes	characteristic
346	C₂×C₁₃₁	#3513	1	4	yes	—
347	#34238	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
348	C₁₃₁	#34238	1	1	yes	characteristic, direct product factor, Sylow
349	C₂²×#123	C₂×C₁₃₁	1	1	yes	characteristic
350	#2374	C₂×C₁₃₁	1	4	yes	complemented
351	#2359	C₂×C₁₃₁	1	4	yes	complemented
352	#2345	C₂×C₁₃₁	1	2	yes	complemented
353	#2342	C₂×C₁₃₁	1	2	yes	complemented
354	#2342	C₂×C₁₃₁	1	2	yes	complemented
355	D₄×C₂²⋊C₄	C₂×C₁₃₁	1	2	yes	—
356	#2335	C₂×C₁₃₁	1	4	yes	complemented
357	#2313	C₂×C₁₃₁	1	1	yes	characteristic, complemented
358	#2312	C₂×C₁₃₁	1	1	yes	characteristic, complemented
359	C₄×#123	C₂×C₁₃₁	1	4	yes	complemented
360	#2280	C₂×C₁₃₁	1	1	yes	characteristic, complemented
361	#2274	C₂×C₁₃₁	1	1	yes	characteristic, complemented
362	#2273	C₂×C₁₃₁	1	1	yes	characteristic, complemented
363	C₂×C₄×C₂²⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
364	C₂³×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
365	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
366	C₂×#123	C₄×C₁₃₁	1	16	yes	complemented
367	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
368	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
369	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
370	C₂×#123	C₂²×C₁₃₁	1	2	yes	—
371	C₂×C₄×D₄	C₂²×C₁₃₁	1	4	yes	—
372	C₂×#117	C₂²×C₁₃₁	1	2	yes	—
373	C₂×#117	C₂²×C₁₃₁	1	2	yes	complemented
374	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
375	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
376	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
377	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
378	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
379	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
380	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
381	C₂²×C₄²	C₂²×C₁₃₁	1	2	yes	complemented
382	#390	C₂²×C₁₃₁	1	4	yes	—
383	#389	C₂²×C₁₃₁	1	4	yes	complemented
384	#388	C₂²×C₁₃₁	1	4	yes	complemented
385	#388	C₂²×C₁₃₁	1	4	yes	complemented
386	#388	C₂²×C₁₃₁	1	4	yes	complemented
387	#388	C₂²×C₁₃₁	1	4	yes	complemented
388	#388	C₂²×C₁₃₁	1	4	yes	complemented
389	#388	C₂²×C₁₃₁	1	4	yes	complemented
390	#387	C₂²×C₁₃₁	1	4	yes	complemented
391	#387	C₂²×C₁₃₁	1	4	yes	complemented
392	#387	C₂²×C₁₃₁	1	4	yes	complemented
393	#387	C₂²×C₁₃₁	1	4	yes	complemented
394	#386	C₂²×C₁₃₁	1	4	yes	—
395	#386	C₂²×C₁₃₁	1	4	yes	—
396	#385	C₂²×C₁₃₁	1	4	yes	complemented
397	#385	C₂²×C₁₃₁	1	4	yes	complemented
398	#381	C₂²×C₁₃₁	1	2	yes	—
399	#381	C₂²×C₁₃₁	1	2	yes	complemented
400	#380	C₂²×C₁₃₁	1	2	yes	—
401	#380	C₂²×C₁₃₁	1	2	yes	—
402	#380	C₂²×C₁₃₁	1	2	yes	—
403	#380	C₂²×C₁₃₁	1	2	yes	complemented
404	#379	C₂²×C₁₃₁	1	2	yes	—
405	#379	C₂²×C₁₃₁	1	2	yes	—
406	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
407	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
408	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
409	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
410	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
411	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
412	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
413	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
414	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
415	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
416	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
417	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
418	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
419	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
420	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	4	yes	complemented
421	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
422	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	complemented
423	C₂×#95	C₂²×C₁₃₁	1	2	yes	complemented
424	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
425	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
426	C₂²×D₄	—	4	4	no	—
427	C₂²×D₄	C₂×C₄×C₁₃₁	1	8	yes	—
428	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
429	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
430	C₂³×C₄	—	4	4	no	—
431	C₂³×C₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
432	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
433	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
435	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
437	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
438	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
441	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
442	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
443	#123	C₂×C₄×C₁₃₁	1	16	yes	complemented
444	#123	C₂×C₄×C₁₃₁	1	16	yes	complemented
445	#123	C₂×C₄×C₁₃₁	1	16	yes	complemented
446	#123	C₂×C₄×C₁₃₁	1	16	yes	complemented
447	C₄×D₄	—	4	8	no	—
448	#117	—	2	8	no	—
449	#117	—	4	4	no	—
450	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
451	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
452	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
453	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
456	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
460	C₂×C₂²⋊C₄	—	2	8	no	—
461	C₂×C₂²⋊C₄	—	2	8	no	—
462	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
463	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
464	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
465	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	2	yes	—
481	C₂×C₄²	—	4	4	no	—
482	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
483	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
484	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
485	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
486	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
487	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
488	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
489	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
490	#95	C₂³×C₁₃₁	1	2	yes	—
491	#95	C₂³×C₁₃₁	1	4	yes	—
492	#95	C₂³×C₁₃₁	1	2	yes	—
493	#95	C₂³×C₁₃₁	1	2	yes	—
494	#95	C₂³×C₁₃₁	1	4	yes	—
495	#95	C₂³×C₁₃₁	1	2	yes	—
496	#95	C₂³×C₁₃₁	1	4	yes	—
497	#95	C₂³×C₁₃₁	1	4	yes	—
498	#95	C₂³×C₁₃₁	1	4	yes	—
499	#95	C₂³×C₁₃₁	1	4	yes	—
500	#95	C₂³×C₁₃₁	1	4	yes	—
501	#95	C₂³×C₁₃₁	1	4	yes	—
502	C₂⁴	—	2	4	no	—
503	C₂⁴	—	2	4	no	—
504	C₂⁴	—	2	4	no	—
505	C₂⁴	—	4	2	no	—
506	C₂⁴	—	4	2	no	—
507	C₂⁴	—	4	2	no	—
508	C₂⁴	C₂²×C₄×C₁₃₁	1	4	yes	—
509	C₂⁴	C₂²×C₄×C₁₃₁	1	4	yes	—
510	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
511	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
512	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
513	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
514	C₂×D₄	—	2	8	no	—
515	C₂×D₄	—	4	4	no	—
516	C₂×D₄	—	4	16	no	—
517	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
518	C₂×D₄	C₂²×C₄×C₁₃₁	1	8	yes	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	2	8	no	—
523	C₂²×C₄	—	2	8	no	—
524	C₂²×C₄	—	2	8	no	—
525	C₂²×C₄	—	4	16	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	4	2	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	4	no	—
532	C₂²×C₄	—	4	2	no	—
533	C₂²×C₄	—	4	4	no	—
534	C₂²×C₄	—	4	4	no	—
535	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
536	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
537	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
538	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
539	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
540	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
541	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
542	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
543	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
544	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
545	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
546	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
547	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
555	C₄⋊C₄	—	2	8	no	—
556	C₄⋊C₄	—	4	4	no	—
557	C₄⋊C₄	—	4	4	no	—
558	C₄⋊C₄	—	4	4	no	—
559	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
560	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
561	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
562	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
563	C₂²⋊C₄	—	2	4	no	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	4	no	—
566	C₂²⋊C₄	—	2	8	no	—
567	C₂²⋊C₄	—	2	8	no	—
568	C₂²⋊C₄	—	2	8	no	—
569	C₂²⋊C₄	—	4	4	no	—
570	C₂²⋊C₄	—	4	4	no	—
571	C₂²⋊C₄	—	4	4	no	—
572	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
573	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
574	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
575	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
576	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
577	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	8	yes	—
578	C₂²⋊C₄	#41×C₁₃₁	1	8	yes	—
579	C₄²	—	2	8	no	—
580	C₄²	—	4	2	no	—
581	C₄²	—	4	4	no	—
582	C₄²	—	4	2	no	—
583	C₄²	—	4	4	no	—
584	C₄²	—	4	2	no	—
585	C₄²	—	4	2	no	—
586	C₄²	—	4	4	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	8	no	—
592	C₂³	—	2	8	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	4	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	4	no	—
600	C₂³	—	2	8	no	—
601	C₂³	—	4	4	no	—
602	C₂³	—	4	4	no	—
603	C₂³	—	4	4	no	—
604	C₂³	—	4	16	no	—
605	C₂³	—	8	8	no	—
606	C₂³	C₂³×C₄×C₁₃₁	1	4	yes	—
607	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
608	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
609	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
610	C₂³	C₂×#41×C₁₃₁	1	4	yes	—
611	C₂³	H(5,𝔽₂)×C₁₃₁	1	4	yes	—
612	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
613	D₄	—	2	16	no	—
614	D₄	—	4	8	no	—
615	C₂×C₄	—	2	8	no	—
616	C₂×C₄	—	2	8	no	—
617	C₂×C₄	—	2	8	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	4	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	—	4	4	no	—
639	C₂×C₄	—	4	4	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	4	4	no	—
643	C₂×C₄	—	4	16	no	—
644	C₂×C₄	—	8	8	no	—
645	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
646	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
647	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
648	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
649	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
650	C₂×C₄	C₂³×C₄×C₁₃₁	1	2	yes	—
651	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
652	C₂×C₄	C₂×#41×C₁₃₁	1	8	yes	—
653	C₂²	—	2	8	no	—
654	C₂²	—	2	8	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	4	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	4	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	4	16	no	—
666	C₂²	—	4	4	no	—
667	C₂²	—	4	4	no	—
668	C₂²	—	4	4	no	—
669	C₂²	—	8	8	no	—
670	C₂²	C₄×#41×C₁₃₁	1	4	yes	—
671	C₂²	#518×C₁₃₁	1	4	yes	—
672	C₂²	C₂⁴×C₄×C₁₃₁	1	1	yes	characteristic
673	C₂²	C₂²×#41×C₁₃₁	1	2	yes	—
674	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	2	yes	—
675	C₂²	#585×C₁₃₁	1	2	yes	—
676	C₄	—	2	8	no	—
677	C₄	—	2	4	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	4	no	—
683	C₄	—	2	4	no	—
684	C₄	—	4	4	no	—
685	C₄	—	4	4	no	—
686	C₄	—	4	4	no	—
687	C₂	—	2	4	no	—
688	C₂	—	2	4	no	—
689	C₂	—	4	2	no	—
690	C₂	—	4	4	no	—
691	C₂	C₂×C₄×#41×C₁₃₁	1	1	yes	characteristic
692	C₂	C₂×#518×C₁₃₁	1	1	yes	characteristic
693	C₂	#3428×C₁₃₁	1	1	yes	characteristic
694	C₂	#3513×C₁₃₁	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃₁
Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂³×D₄×C₁₃₁	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #2374×C₁₃₁	C₂	semidirect
3. #2359×C₁₃₁	C₂	semidirect
4. #2345×C₁₃₁	C₂	semidirect
5. #2342×C₁₃₁	C₂	semidirect
6. #2342×C₁₃₁	C₂	semidirect
8. #2335×C₁₃₁	C₂	semidirect
9. #2313×C₁₃₁	C₂	semidirect
10. #2312×C₁₃₁	C₂	semidirect
11. C₄×#123×C₁₃₁	C₂	semidirect
12. #2280×C₁₃₁	C₂	semidirect
13. #2274×C₁₃₁	C₂	semidirect
14. #2273×C₁₃₁	C₂	semidirect
15. C₂×C₄×C₂²⋊C₄×C₁₃₁	C₂	semidirect
18. C₂×#123×C₁₃₁	C₄	semidirect
25. C₂×#117×C₁₃₁	C₂²	semidirect
33. C₂²×C₄²×C₁₃₁	C₂²	semidirect
35. #389×C₁₃₁	C₂²	semidirect
36. #388×C₁₃₁	C₂²	semidirect
37. #388×C₁₃₁	C₂²	semidirect
38. #388×C₁₃₁	C₂²	semidirect
39. #388×C₁₃₁	C₂²	semidirect
40. #388×C₁₃₁	C₂²	semidirect
41. #388×C₁₃₁	C₂²	semidirect
42. #387×C₁₃₁	C₂²	semidirect
43. #387×C₁₃₁	C₂²	semidirect
44. #387×C₁₃₁	C₂²	semidirect
45. #387×C₁₃₁	C₂²	semidirect
48. #385×C₁₃₁	C₂²	semidirect
49. #385×C₁₃₁	C₂²	semidirect
51. #381×C₁₃₁	C₂²	semidirect
55. #380×C₁₃₁	C₂²	semidirect
58. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
59. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
60. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
68. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
69. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
70. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
71. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
72. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
73. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
74. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
75. C₂×#95×C₁₃₁	C₂²	semidirect
83. C₂³×C₄×C₁₃₁	C₂×C₄	semidirect
95. #123×C₁₃₁	C₂×C₄	semidirect
96. #123×C₁₃₁	C₂×C₄	semidirect
97. #123×C₁₃₁	C₂×C₄	semidirect
98. #123×C₁₃₁	C₂×C₄	semidirect
102. C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	semidirect
103. C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	semidirect
114. C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	semidirect
115. C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	semidirect
116. C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	semidirect
347. #34238	C₁₃₁	direct (N × H)
348. C₁₃₁	#34238	direct (N × H)
350. #2374	C₂×C₁₃₁	semidirect
351. #2359	C₂×C₁₃₁	semidirect
352. #2345	C₂×C₁₃₁	semidirect
353. #2342	C₂×C₁₃₁	semidirect
354. #2342	C₂×C₁₃₁	semidirect
356. #2335	C₂×C₁₃₁	semidirect
357. #2313	C₂×C₁₃₁	semidirect
358. #2312	C₂×C₁₃₁	semidirect
359. C₄×#123	C₂×C₁₃₁	semidirect
360. #2280	C₂×C₁₃₁	semidirect
361. #2274	C₂×C₁₃₁	semidirect
362. #2273	C₂×C₁₃₁	semidirect
363. C₂×C₄×C₂²⋊C₄	C₂×C₁₃₁	semidirect
366. C₂×#123	C₄×C₁₃₁	semidirect
373. C₂×#117	C₂²×C₁₃₁	semidirect
381. C₂²×C₄²	C₂²×C₁₃₁	semidirect
383. #389	C₂²×C₁₃₁	semidirect
384. #388	C₂²×C₁₃₁	semidirect
385. #388	C₂²×C₁₃₁	semidirect
386. #388	C₂²×C₁₃₁	semidirect
387. #388	C₂²×C₁₃₁	semidirect
388. #388	C₂²×C₁₃₁	semidirect
389. #388	C₂²×C₁₃₁	semidirect
390. #387	C₂²×C₁₃₁	semidirect
391. #387	C₂²×C₁₃₁	semidirect
392. #387	C₂²×C₁₃₁	semidirect
393. #387	C₂²×C₁₃₁	semidirect
396. #385	C₂²×C₁₃₁	semidirect
397. #385	C₂²×C₁₃₁	semidirect
399. #381	C₂²×C₁₃₁	semidirect
403. #380	C₂²×C₁₃₁	semidirect
406. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
407. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
408. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
416. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
417. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
418. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
419. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
420. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
421. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
422. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
423. C₂×#95	C₂²×C₁₃₁	semidirect
431. C₂³×C₄	C₂×C₄×C₁₃₁	semidirect
443. #123	C₂×C₄×C₁₃₁	semidirect
444. #123	C₂×C₄×C₁₃₁	semidirect
445. #123	C₂×C₄×C₁₃₁	semidirect
446. #123	C₂×C₄×C₁₃₁	semidirect
450. C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	semidirect
451. C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	semidirect
462. C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	semidirect
463. C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	semidirect
464. C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#123×C₁₃₁	2
#2374×C₁₃₁	2
#2359×C₁₃₁	2
#2345×C₁₃₁	2
#2342×C₁₃₁	2
D₄×C₂²⋊C₄×C₁₃₁	2
#2335×C₁₃₁	2
#2313×C₁₃₁	2
#2312×C₁₃₁	2
C₄×#123×C₁₃₁	2
#2280×C₁₃₁	2
#2274×C₁₃₁	2
#2273×C₁₃₁	2
C₂×C₄×C₂²⋊C₄×C₁₃₁	2
#34238	131

Subgroups — C131×#34238 #45720122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#34238 #45720122